Quantum confined laser devices: optical gain and recombination in semiconductors
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2015
|
| Edition: | 1. ed. |
| Series: | Oxford master series in physics
23 : atomic, optical, and laser physics |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVI, 405 S. graph. Darst. |
| ISBN: | 9780199644513 9780199644520 0199644527 |
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| 245 | 1 | 0 | |a Quantum confined laser devices |b optical gain and recombination in semiconductors |c Peter Blood |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2015 | |
| 300 | |a XXVI, 405 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Oxford master series in physics |v 23 : atomic, optical, and laser physics | |
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| adam_text | Contents
About this book xix
List of symbols xxi
i The beginning 1
1.1 The maser and laser 1
1.2 What is a laser? 2
1.3 The semiconductor laser 3
1.4 Quantum confinement 5
1.5 Laser diode timeline 6
Further reading 7
Part I The diode laser
2 Introduction to optical gain 11
2.1 Stimulated emission and optical gain 11
2.1.1 Stimulated emission 11
2,1.2 Optical gain coefficient 12
2.2 Gain and absorption 13
2.3 Inversion and occupation statistics 14
2.3.1 Gain in a laser diode 14
2.3.2 Thermal equilibrium 14
2.3.3 Population inversion and quasi-equilibrium 15
2.3.4 Holes 16
2.3.5 Carrier distributions 16
2.4 Condition for gain 17
2.5 Gain spectra and transparency 18
2.6 Laser diode structure 19
Chapter summary 20
Further reading 21
Exercises 21
3 The laser diode structure 22
3.1 Epitaxial layers and strain 22
3.2 III-V compound semiconductors 23
3.3 III-V semiconductor alloys 25
3.3.1 AlGaAs on GaAs (0.87-0.70 pm) 25
3.3.2 GalnP on GaAs (0.65 pm) and GalnÀs
on InP (1.55 pm)
25
Vlll
Contents
3.3.3 AlGalnP on GaAs (red emission) 26
3.3.4 GalnAs(N) on GaAs (1-1.3 pm) 26
3.3.5 AlGalnN (blue emission) 27
3.4 Energy band diagrams of heterostructures 27
3.4.1 Isotype heterostructure: band offsets 27
3.4.2 Isotype double heterobarrier: the quantum well 29
3.4.3 The double heterojunction 30
3.4.4 Energy band diagram of a diode laser 31
3.5 Practical matters 32
3.5.1 Formation of wells and dots 32
3.5.2 Technology 32
Chapter summary 33
Further reading 33
Exercises 34
4 The planar waveguide 35
4.1 Electromagnetic waves and modes 35
4.1.1 In a non-dispersive isotropic dielectric 35
4.1.2 In a waveguide 36
4.1.3 TE and TM waveguide modes: the weak
guiding approximation 37
4.1.4 Energy flux in a waveguide 37
4.1.5 Labelling of modes 38
4.1.6 Near- and far-held distributions 39
4.2 Transverse modes of the slab waveguide 39
4.2.1 Maxwell’s equations 39
4.2.2 Allowed transverse modes 42
4.3 Material gain and modal gain 43
4.3.1 Gain material alone 43
4.3.2 Gain material in a waveguide 44
4.4 A quantum confined layer 44
4.4.1 Material gain of a quantum well 44
4.4.2 Modal gain 45
4.4.3 The confinement factor 46
4.4.4 Effective mode width 46
4.4.5 Maximising coupling to the mode 47
4.4.6 Nano-lasers and the confinement factor 47
4.5 Interna] optical mode loss 47
Chapter summary 48
Further reading 48
Exercises 49
5 Laser action 50
5.1 Amplification and threshold 50
5.1.1 The spontaneous emission factor 50
5.1.2 Single-pass amplification 50
5.1.3 Round-trip amplification 51
Contents ix
5.2 Laser threshold 51
5.2.1 Field amplitude condition: threshold gain 52
5.2.2 Phase condition: longitudinal modes 53
5.2.3 Optical field above threshold 54
5.2.4 Fermi level pinning in a laser 54
5.3 Threshold current 55
5.3.1 Assumptions 55
5.3.2 Recombination 55
5.3.3 Recombination current at threshold 56
5.4 Gain-current relation 57
5.5 Efficiency 58
5.5.1 Quantum efficiency at and below threshold 58
5.5.2 Above threshold: light extraction
and differential quantum efficiency 60
5.5.3 Power conversion efficiency 61
5.6 The gain medium and the laser 62
Chapter summary 63
Further reading 63
Exercises 63
Part II Fundamental processes
6 The classical atomic dipole oscillator 67
6.1 Introduction 67
6.2 Classical dipole oscillators 67
6.3 Gain and the complex susceptibility 68
6.3.1 Properties of linear dielectrics 68
6.3.2 Maxwell’s equations 69
6.3.3 Dipole response 71
6.4 The classical atomic oscillator 71
6.4.1 Microscopic polarisation 72
6.4.2 Macroscopic polarisation of an ensemble 73
6.5 Complex susceptibility of an ensemble 76
6.5.1 Optical absorption 77
6.5.2 Linewidth: homogeneous broadening 79
6.6 Measures of optical absorption 80
6.6.1 Optical cross section 80
6.6.2 Absorption coefficient 81
6.6.3 Integrated optical cross section 81
6.6.4 Applicability 82
Chapter summary 82
Further reading 83
Exercises 83
7 Quantum mechanical interaction of light with atoms 85
7.1 Introduction 85
7.2 The Einstein coefficients 85
7.2.1 Rate equations 85
7.2.2 Atoms in a blackbody cavity 87
x Contents
7.2.3 Relation to the optical cross section 89
7.2.4 Insights 90
7.3 Time-dependent Schrödinger equation 90
7.3.1 Coherent superposition of states 91
7.3.2 Perturbation and probability amplitudes 92
7.3.3 Weak-field limit 94
7.3.4 Wavefunction dephasing 96
7.3.5 Transition rates 98
7.3.6 Rabi oscillations 98
7.3.7 Homogeneous linewidth: T and T2 times 99
7.4 Einstein relations and the optical cross section 100
7.4.1 Optical cross section 100
7.4.2 Einstein coefficient 101
7.5 A one-dimensional atom 101
7.5.1 Wavefunctions 101
7.5.2 Dipole moment and matrix element 103
7.5.3 Time dependence of the atomic dipole 103
7.5.4 Where is the dipole? 104
7.6 Dipoles in three dimensions 105
7.7 Momentum matrix element and Fermi’s Golden Rule 105
Chapter summary 107
Further reading 108
Exercises 108
8 Quantum confinement 110
8.1 Introduction 110
8.2 Electron states in crystals 110
8.2.1 Bonds and bands 110
8.2.2 Bloch’s theorem in macroscopic crystals 111
8.2.3 Bloch’s theorem in quantum confined structures 113
8.3 The one-dimensional infinitely deep well 114
8.4 Schrödinger’s equation for a finite
one-dimensional square well 115
8.4.1 Method of solution 115
8.4.2 Solutions for a one-dimensional well 117
8.5 Quantum dot models 119
8.5.1 Quantum box 119
8.5.2 Harmonic potential 121
8.6 Quantum wells 123
8.6.1 Solutions of Schrödinger’s equation 123
8.6.2 Density of states 125
8.6.3 Carrier density 127
8.6.4 Effect of the well width 128
8.7 Confined states and extended states 129
Chapter summary 129
Further reading 130
Exercises 130
Contents xi
Part III Device physics
9 Gain and emission in quantum dots 135
9.1 Introduction 135
9.2 Optical transitions in dots 136
9.2.1 A single dot 136
9.2.2 An ensemble of identical dots; normal incidence 138
9.2.3 Normal incidence: inhomogeneous dots 139
9.3 Absorption and gain in a waveguide 141
9.3.1 Absorption: homogeneous dots 141
9.3.2 Gain: inhomogeneous dots 142
9.3.3 Modal absorption spectrum 143
9.4 Material gain of dots 143
9.5 Polarisation and spontaneous emission 145
9.5.1 Polarisation dependence of the matrix element 145
9.5.2 Spontaneous emission 145
9.6 Occupation probability of dot states 147
9.6.1 Global neutrality and independent population 148
9.6.2 Correlated population 149
9.6.3 Random population 149
9.6.4 For the purposes of this book ... 151
9.7 Modal gain and emission spectra 151
9.7.1 Modal gain spectra 152
9.7.2 Spontaneous emission spectra 152
9.8 Gain-current characteristics at 300 K 153
9.9 Temperature dependence of threshold current 155
9.10 Coulomb interactions 156
9.11 Concluding remarks 156
Chapter summary 157
Further reading 157
Exercises 158
10 Rate equations for dot state occupation 159
10.1 Introduction 159
10.1.1 Steady state and equilibrium 159
10.1.2 Carrier distributions 159
10.1.3 Rate equation models 160
10.2 Rate equation models 160
10.3 Ground states 161
10.3.1 General rate equations 161
10.3.2 High temperatures 164
10.3.3 Low temperatures 165
10.3.4 Device current 165
10.3.5 An example 166
10.3.6 General observations 167
10.4 Ground and excited states 167
10.4.1 Rate equation model 167
10.4.2 An example 168
xii Contents
10.5 Concluding remarks 169
Chapter summary 170
Further reading 170
Exercises 170
11 Optical transitions in quantum wells 172
11.1 Introduction 172
11.2 Wavefunctions and transition rates 172
11.2.1 Wavefunctions 173
11.2.2 Perturbation 173
11.2.3 Transition rate 174
11.2.4 ^-selection 175
11.2.5 The transition density 175
11.2.6 Transitions between sub-bands 177
11.2.7 Overlap integral: selection rules 177
11.3 Matrix element, valence bands, and polarisation 178
11.3.1 Momentum matrix element 178
11.3.2 Relation to the band structure 180
11.3.3 Polarisation 180
11.3.4 Recapitulation on momentum matrix elements 182
11.3.5 Relevance to quantum dots 183
11.4 Absorption by quantum wells at normal incidence 183
11.4.1 Fraction of light absorbed 183
11.4.2 General features of the absorption spectrum 184
11.4.3 Experimental measurements of absorption 185
11.5 Modal gain in a slab waveguide 185
11.5.1 The general result 186
11.5.2 Thin wells 187
11.5.3 Approximation for rectangular wells 188
11.5.4 Homogeneous broadening 188
11.5.5 Modal and material gain 189
11.6 Radiative recombination in wells 189
11.6.1 Spontaneous emission spectrum 189
11.6.2 Spontaneous emission and the
recombination coefficient 191
Chapter summary 192
Further reading 192
Exercises 193
12 Gain and recombination current in quantum wells 195
12.1 Introduction 195
12.2 Modal gain and emission spectra 195
12.2.1 Energy levels and wavefunctions 195
12.2.2 Modal gain 195
12.2.3 Spontaneous emission spectra 197
12.3 Gain and radiative current 198
12.3.1 Gain-current curves 198
12.3.2 Current contributions 198
Contents
Xlll
12.3.3 Algebraic approximation 199
12.3.4 Effect of the well width 199
12.3.5 Inhomogeneous broadening: well width
fluctuations 200
12.3.6 Non-parabolic bands 200
12.4 Effect of temperature 201
12.4.1 Gain 202
12.4.2 Emission, carrier density, and
recombination current 203
12.5 Strain 204
12.5.1 A bulk layer 205
12.5.2 Strained quantum well 206
12.5.3 Consequences for laser operation 206
12.6 Many-body Coulomb effects 208
12.6.1 Band gap narrowing 209
12.6.2 Coulomb enhancement 211
12.6.3 Dephasing time 211
12.6.4 Effect on device operation 211
Chapter summary 212
Further reading 213
Exercises 213
13 Rate equations for laser operation 215
13.1 Formulation of the photon and carrier rate equations 215
13.2 Steady-state solutions 218
13.2.1 The steady-state equations 218
13.2.2 Light-current curve 218
13.2.3 Spontaneous emission and threshold 219
13.2.4 The influence of /3spon 220
13.2.5 Cavity round-trip time 220
13.2.6 Intraband relaxation 221
13.3 Laser operation of quantum dots 221
13.3.1 Quasi-equilibrium 221
13.3.2 Rate equations for a non-thermal carrier
distribution 221
13.4 Small signal modulation 225
13.4.1 Small signal equations 226
13.4.2 Modulation response 227
13.4.3 The resonance or relaxation frequency 229
13.4.4 Gain compression 229
13.5 Carrier transport 230
13.5.1 Transport time 230
13.5.2 Rate equations 231
13.5.3 Solution 231
13.6 What is a laser? 233
Chapter summary 235
Further reading 235
Exercises 235
Contents
Part IV Device operation
14 Device structures 239
14.1 Classification of device structures 239
14.2 Stripe laser 240
14.2.1 Current spreading 240
14.2.2 Optical modes 240
14.2.3 Pros and cons of stripe lasers 240
14.3 Ridge waveguide lasers 241
14.4 Grating feedback devices 241
14.4.1 In-plane devices 242
14.4.2 Vertical-cavity surface-emitting lasers (VCSELs) 243
14.5 Properties of gratings 244
14.5.1 Bragg gratings 244
14.5.2 Reflectivity 245
14.6 Threshold of in-plane grating lasers 247
14.6.1 DBR laser threshold 247
14.6.2 DFB laser threshold 249
14.7 Components of a VCSEL 249
14.7.1 Bragg stacks: the effective mirror 249
14.7.2 The cavity 251
14.7.3 Quantum wells 251
14.8 VCSEL threshold 251
14.8.1 A model for the VCSEL 251
14.8.2 Optical losses 252
14.8.3 Coupling to the optical field 253
14.8.4 Threshold 255
14.8.5 Mode selection in grating lasers 256
Chapter summary 256
Further reading 257
Exercises 257
15 Threshold and the light-current characteristic 259
15.1 The light-current curve 259
15.1.1 Measurement of the light-current curve 259
15.1.2 Threshold current density 260
15.1.3 Differential quantum efficiency 262
15.2 Non-radiative and leakage currents 262
15.3 Recombination in the gain layer 263
15.3.1 Shockley -Read Hall recombination 263
15.3.2 Radiative recombination 265
15.3.3 Auger recombination 265
15.3.4 Recombination current in the gain layer 267
15.4 Total device current 267
15.5 Evidence for non-radiative processes in a quantum well 268
15.5.1 Sub-threshold L~I curve: a light-emitting diode 268
15.5.2 Power law analysis in a well 269
15.5.3 A health warning 270
Contents xv
15.6 Cavity length dependence; quantum well lasers 271
15.6.1 Threshold current density 271
15.6.2 Threshold current 272
15.6.3 Internal differential quantum efficiency
and optical mode loss 273
15.7 Dependence on the number of wells 277
15.8 Quantum dot lasers 277
15.8.1 Differential efficiency and optical loss 278
15.8.2 Recombination and leakage in dot lasers 278
15.8.3 Recombination in the dot layer 278
15.8.4 Wetting layer recombination and efficiency 280
Chapter summary 281
Further reading 282
Exercises 282
16 Temperature dependence of threshold current 284
16.1 The context 284
16.1.1 Dimensionality 284
16.1.2 Gain, Fermi levels, and recombination 285
16.2 Quantum dot lasers 286
16.2.1 Processes in the dots 286
16.2.2 Recombination in the wetting layer 286
16.2.3 Temperature dependence of the maximum gain 287
16.2.4 Dot lasers at low temperature 288
16.2.5 Summary: Dot active regions 290
16.3 Quantum well lasers 290
16.3.1 Modal gain and Fermi levels 290
16.3.2 Recombination in the well 291
16.3.3 Barrier recombination: direct and indirect gaps 292
16.3.4 Summary: quantum well active regions 294
16.4 Leakage through the cladding layer 294
16.4.1 Diffusion 295
16.4.2 Drift 296
16.4.3 Drift and diffusion 297
16.4.4 Analysis of the differential quantum efficiency 299
16.5 Analysis of temperature dependence 299
16.6 Temperature-dependent optical loss 300
16.7 Grating feedback: the VCSEL 301
16.8 The characteristic temperature: To 301
16.9 Concluding remarks 303
Chapter summary 304
Further reading 304
Exercises 304
Part V Studies of gain and recombination
17 Measurement of gain and emission 309
17.1 Round-trip, cavity length method 309
17.2 The Hakki-Paoli round-trip method 310
XVI
Contents
17.2.1 Fabry-Perot fringes 310
17.2.2 Implementation 312
17.2.3 Practical aspects 312
17.2.4 Refinements 313
17.3 Window observation of spontaneous emission 314
17.3.1 Motivation 314
17.3.2 Structures 314
17.3.3 Applications 315
17.4 Optical gain from spontaneous emission spectra 315
17.4.1 Relation between gain and emission
for a quantum well 316
17.4.2 Transformation of emission to gain 317
17.4.3 Gain and recombination current 319
17.4.4 Examples 319
17.5 Application to dots 321
17.6 Concluding remarks 321
Chapter summary 321
Further reading 322
Exercises 322
18 Single-pass measurement of gain and emission 323
18.1 Survey of single-pass methods 323
18.1.1 Optical excitation 323
18.1.2 Optical travelling spot measurement
of mode loss 324
18.1.3 Electrical excitation 325
18.1.4 Electrical segmented contact method 325
18.2 Electrical segmented contact method 326
18.2.1 Single-pass ASE 326
18.2.2 Two identical segments 328
18.2.3 Derived gain and emission spectra 329
18.3 The internal spontaneous emission rate 330
18.3.1 The population inversion factor 330
18.3.2 Calibration of the emission rate 331
18.3.3 Radiative current and internal efficiency 332
18.4 Gain-current relation 332
18.5 The population inversion factor 333
18.6 Requirements and refinements 334
18.6.1 Unamplified light 334
18.6.2 Three-section method 335
18.6.3 Longitudinal current spreading 336
18.6.4 Photogenerated light 337
18.7 Comparisons and assessment 337
Chapter summary 338
Further reading 338
Exercises 338
Contents
XVII
Appendices
A Trends with band gap 339
A.l The matrix element 339
A.2 Gain and emission 340
A. 3 Optical cross section 342
B The Boltzmann approximation 344
B. l The approximation 344
B.2 Carrier densities in quantum wells 345
B.3 Spontaneous emission spectra 346
B.4 Spectrally integrated spontaneous emission rate 347
B. 5 The two-dimensional radiative recombination coefficient 349
C Carrier interactions: excitons and Coulomb
enhancement 352
C. l In three dimensions 352
C.1.1 Bound states: excitons 352
C.l.2 Coulomb enhancement: the Sommerfeld factor 354
C.2 Quantum wells 355
C.2.1 Bound exciton states 356
C.2.2 Continuum states 356
C.2.3 Wells of finite depth 357
C.3 Quantum dots 357
C. 4 Conclusions: laser structures 359
Further reading 360
D Multilayer Bragg reflector 361
D. l Reflection by multiple layers 361
D. 2 Phase change at multilayer reflector 362
E Carrier recombination and lifetime 364
E. l Generation and recombination 364
E.l.l Dynamic equilibrium 364
E.l.2 Excess carriers 364
E.l.3 General solution for the decay 365
E.l.4 Doped semiconductor: minority carriers 365
E.2 Carrier lifetime 366
E.2.1 The minority carrier lifetime 366
E.2.2 The differential lifetime 367
E.3 Radiative recombination 367
E.3.1 Low injection, or high doping 368
E.3.2 High injection 368
E.4 Shockley-Read-Hall (SRH) recombination 368
E.4.1 The SRH recombination process 368
E.4.2 SRH recombination rate and lifetime 369
E.4.3 Carrier capture in three dimensions 371
E.4.4 Carrier capture from a two-dimensional system 372
XVIII
Contents
E.4.5 Characterisation of deep states 372
E.4.6 Deep state density 372
E.5 Auger recombination 373
E.5.1 The CCCH process 373
E.5.2 Other Auger processes: the CHSH process 375
E. 6 Concluding remarks 376
Further reading 376
F Arrhenius plots 377
F. l Arrhenius plots 377
F.2 Temperature dependence of barrier emission at threshold 377
F.3 SRH recombination across the indirect gap 379
F.4 General thermodynamic treatment 380
F.5 Quasi-Fermi level separation 381
F.6 Conclusions 381
Further reading 382
G Henry’s derivation of spontaneous emission and gain 383
References 387
Index 399
|
| any_adam_object | 1 |
| author | Blood, Peter |
| author_GND | (DE-588)107929192X |
| author_facet | Blood, Peter |
| author_role | aut |
| author_sort | Blood, Peter |
| author_variant | p b pb |
| building | Verbundindex |
| bvnumber | BV042723570 |
| classification_rvk | UH 5616 UP 3150 |
| classification_tum | PHY 373f |
| ctrlnum | (OCoLC)932840731 (DE-599)BVBBV042723570 |
| discipline | Physik |
| edition | 1. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV042723570 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:08:13Z |
| institution | BVB |
| isbn | 9780199644513 9780199644520 0199644527 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028154721 |
| oclc_num | 932840731 |
| open_access_boolean | |
| owner | DE-20 DE-29T DE-91G DE-BY-TUM DE-11 DE-703 |
| owner_facet | DE-20 DE-29T DE-91G DE-BY-TUM DE-11 DE-703 |
| physical | XXVI, 405 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford master series in physics |
| series2 | Oxford master series in physics |
| spelling | Blood, Peter Verfasser (DE-588)107929192X aut Quantum confined laser devices optical gain and recombination in semiconductors Peter Blood 1. ed. Oxford Oxford Univ. Press 2015 XXVI, 405 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford master series in physics 23 : atomic, optical, and laser physics Quantenpunktlaser (DE-588)4767124-5 gnd rswk-swf Quantenwell-Laser (DE-588)4300724-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenwell-Laser (DE-588)4300724-7 s DE-604 Quantenpunktlaser (DE-588)4767124-5 s Oxford master series in physics 23 : atomic, optical, and laser physics (DE-604)BV017064373 23 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028154721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blood, Peter Quantum confined laser devices optical gain and recombination in semiconductors Oxford master series in physics Quantenpunktlaser (DE-588)4767124-5 gnd Quantenwell-Laser (DE-588)4300724-7 gnd |
| subject_GND | (DE-588)4767124-5 (DE-588)4300724-7 (DE-588)4123623-3 |
| title | Quantum confined laser devices optical gain and recombination in semiconductors |
| title_auth | Quantum confined laser devices optical gain and recombination in semiconductors |
| title_exact_search | Quantum confined laser devices optical gain and recombination in semiconductors |
| title_full | Quantum confined laser devices optical gain and recombination in semiconductors Peter Blood |
| title_fullStr | Quantum confined laser devices optical gain and recombination in semiconductors Peter Blood |
| title_full_unstemmed | Quantum confined laser devices optical gain and recombination in semiconductors Peter Blood |
| title_short | Quantum confined laser devices |
| title_sort | quantum confined laser devices optical gain and recombination in semiconductors |
| title_sub | optical gain and recombination in semiconductors |
| topic | Quantenpunktlaser (DE-588)4767124-5 gnd Quantenwell-Laser (DE-588)4300724-7 gnd |
| topic_facet | Quantenpunktlaser Quantenwell-Laser Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028154721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017064373 |
| work_keys_str_mv | AT bloodpeter quantumconfinedlaserdevicesopticalgainandrecombinationinsemiconductors |